Probability distribution relationships

In 1986, Lawrence Leemis published a paper containing a diagram of 43 probability distribution families. The diagram summaries connections between the distributions with arrows: chi-squared is a special case of gamma, Poisson is a limiting case of binomials, the ratio of two standard normals is a Cauchy, etc. It’s a very handy reference, a sort of periodic table for statisticians. His diagram and variations have appeared in several text books over the last 20 years, such as Casella and Berger.

Now Leemis has published an expanded version containing 76 probability distributions. The paper is in the February 2008 issue of American Statistician and is also available online. The heart of the article is the diagram on page 3.